Wikipedia is one of the mainstays of online resources these days. Not only has it collected authoritative information about a particular subject, but in the process of enriching its content, it has created several paradigms of wiki-style writing. As an example, when Wikipedia expounds on a particular scientific or sociological theory, it presents the main idea of the theory, its history, applicability, proponents and opponents, the last of which is a signature component of wiki-style writing that distinguishes itself from usual textbooks on a subject, which tends to be highly favorably biased. One curious fact has been observed, however, that when it comes to mathematical theories, perhaps because of the ostensible a priori notion that math is beyond any doubt correct, they are left unscathed by any section of criticism, as if the theories are themselves directly descend from gods and are completely immune to human judgment. If you ask most career mathematician during private conversation on what his or her opinion is about certain subject, I am sure the answer is not universally favorable. Take category theory as an example, a certain percentage of analysts and I’d say a good number of applied mathematicians, would not be too impressed by its development in recent decades, whose main source of inspiration seems to stem from Algebraic geometry, a branch largely viewed as created by a few founding father figures like Grothendieck, Serre, H. Cartan, Leray. Granted, some says the proof of Fermat’s last theorem would not have come into being without the language of category theory. That nevertheless by itself is a pretty subjective statement, and at the risk of sounding naive, just like humans have a multitude of spoken and written languages, perhaps category is not the unique path, and more importantly, perhaps the necessity of the theory in grappling with world class open problems can be better expounded by experts, a task that would certainly prove a lot more pivotal in the field than the resolution of a deep theorem itself.
So back to the discussion on wikipedia entries, the void of criticism on mathematical theories seems likely to embolden self-proclaimed theorists to continue engaging in their sometimes aimless abstract dream-weaving, while isolating them further from the rest of the intellectual world. Granted many of them are probably having a hard time getting fundings to fuel their research, they still do exist in large quantities and occupy a centerpiece in the ivory tower of math. This niche of comfortable living warrants an equally harsh section of nay-sayers and negative feedbacks on such an objective platform as our beloved wikipedia (to which I donate regularly). Of course my own perception of uselessness of the subject does not preclude others from thinking otherwise. But that is precisely the point of allowing negativity in presenting the subject. Presumably given the self-absorbed nature of elite category theorists, only when they are truly confronted externally by dissenters and disapprovers could one hope that they will lift their eyes and say one or two things about how their theory helped transform the world of mathematics, if not the world at large. Again this poignant little piece of mine might be taken quite offensively by some, many not even directly associated with category theory, but my goal is indeed to illicit such convulsive reaction. But category theory is only a digression into the main topic, namely math should be treated with skepticism just like other subjects are. Only so can ordinary mortals seek to come on par with its line of reasoning, and hence hope one day to master a small piece of it.